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A Piezoelectric Finite Shell Element for the Geometrically Nonlinear Analysis of Sensors
Author(s) -
Schulz Katrin,
Klinkel Sven,
Wagner Werner
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810337
Subject(s) - shell (structure) , finite element method , piezoelectricity , electric field , nonlinear system , displacement field , constitutive equation , dielectric , electric displacement field , variational principle , displacement (psychology) , node (physics) , bending , mathematical analysis , geometry , mechanics , classical mechanics , physics , materials science , mathematics , engineering , structural engineering , acoustics , composite material , psychology , optoelectronics , quantum mechanics , psychotherapist
A geometrically nonlinear finite element formulation to analyze piezoelectric shell structures is presented. The formulation is based on the mixed field variational functional of Hu–Washizu. Within this variational principle the independent fields are displacements, electric potential, strains, electric field, stresses and dielectric displacements. The mixed formulation allows an interpolation of the strains and the electric field through the shell thickness, which is an essential advantage when using a three dimensional material law. It is remarked that no simplification regarding the constitutive relation is assumed. The normal zero stress condition and the normal zero dielectric displacement condition are enforced by the independent resultant stress and resultant dielectric displacement fields. The shell structure is modeled by a reference surface with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed mixed hybrid shell element fulfills the in–plane, bending and shear patch tests, which have been adopted for coupled field problems. A numerical investigation of a smart antenna demonstrates the applicability of the piezoelectric shell element under the consideration of geometrical nonlinearity. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)